A noncontact three-dimensional measuring system, which is also called a range finder, is capable of high-speed measurement as compared with a contact measuring system and is found particularly advantageous when used to measure a body contour, to allow a robot to visually recognize an object, or to input data to a CG (Computer Graphics) system or a CAD (Computer Aided Design) system.
As a method of obtaining a three-dimensional image of an object by optically scanning it, it is known to use light beams filtering through a slit aperture in a range finder and consequently being of rectilinear cross-section. This method is called a light section method, which is characterized in that the object is actively irradiated by light beams. The three-dimensional image obtained by this method is an aggregate of the three-dimensional positions of points disposed on the surface of the object.
FIGS. 25(a-d) provide diagrammatic illustrations of the aforesaid method. FIGS. 26(a-c) are diagrams for the principle of measurement to be carried out by the aforesaid method.
FIGS. 25(a-d) are based on the assumption that the shape of an object Q is going to be measured. For this purpose, the object Q is irradiated by a thin strip of light beams U. Reflected light beams are directed to the image pickup surface S2 of a two-dimensional image sensor (FIG. 25(a)). A rectilinear image is obtained when a flat portion of the object Q is irradiated (FIG. 25(b)). A curved or step-formed image is obtained when an uneven portion of the object Q is irradiated (FIG. 25(c)). Thus a position on the image pickup surface S2 on which a reflected light beam is incident is determined by the distance between the measuring apparatus and a point on the surface of the object Q at which the light beam is reflected (FIG. 25(d)). In order to take samples of three-dimensional positions from the surface of the object, the thin strip of light beams U is pivoted in a direction which is perpendicular to a virtual plane formed by the thin strip of light beams U. The sample size depends on the number of picture elements provided on the surface of the image sensor.
As shown in FIGS. 26(a-c), the relative positions of a light-emitting assembly including a luminescent spot A and a light-receiving assembly including a principal point O are such that a base line AO connecting the luminescent spot A with the principal point O is perpendicular to a light-receiving axis which in turn is perpendicular to the image pickup surface S2. The principal point O of the lens assembly lies on the light-receiving axis and is disposed away from the image pickup surface S2 by an image distance b, which is the sum of a focal length f and an amount of shift of a lens effected for adjusting the focus thereof.
In FIGS. 26(a-c), the spatial directions are designated by the letters X, Y and Z, where the Z axis is constituted by the light-receiving axis, the Y axis is constituted by the base line AO, and the X axis extends in the direction between the two edges of, i.e. transverse to, the thin strip of light beams U, with an origin constituted by the principal point O. A light beam U irradiating a point P (X, Y, Z) disposed on the surface of the object makes an angle .theta.a with a reference plane passing along the luminescent spot A and extending parallel with the XZ plane. This angle is hereinafter referred to as a "light-emitting angle". On the other hand, by the expression "light-receiving angle" as used herein is meant an angle .theta.p made by the XZ plane with a line connecting the point P with the principal point O. Then the distance L between the luminescent spot A and the principal point O is given by EQU L=L1+L2=Ztan .theta.a+Ztan .theta.p
where L1=distance between the point P and the reference plane
L2=distance between the point P and the XZ plane PA1 Z=Z coordinate of the point P PA1 yp+distance therebetween measured along the Y axis PA1 .beta.=magnification b/Z
Whence, we obtain EQU Z=L/(tan .theta.a+tan .theta.p) (1)
The X and Y coordinates of the point P are given by EQU X=xp/.beta. (2) EQU Y=yp/.beta. (3)
where xp=distance between the image of point P and the center of image pickup surface S2 measured along the X axis
The light-emitting angle .theta.a is determined by an angular velocity at which the thin strip of light beams U is pivoted. The light-receiving angle .theta.p can be calculated from tan .theta.p=yp/b. Therefore, the three-dimensional position of the point P can be found from the measurement of xp, yp and .theta.a.
When a zoom lens assembly having front- and rear-side principal points H and H' is incorporated in the light-receiving assembly as shown in FIG. 26(c), the rear-side principal point H' serves as the aforesaid principal point O. In this case, the Z coordinate of the point P is given by EQU L=L1+L2=Ztan .theta.a+(Z-M)tan .theta.p EQU .thrfore.Z=(L+Mtan .theta.p)/(tan .theta.a+tan .theta.p)
where M=distance between the principal points H and H'
The resolution of a three-dimensional measuring system depends on the density of picture elements arranged on the surface of an image pickup means incorporated in the measuring system. This means that, when an image pickup means such as a CCD (Charge Coupled Device) image sensor having only a limited number of picture elements on the image pickup surface S2 is used, only a limited number of images of points P, which are determined by the xp and yp coordinates on the image pickup surface S2, result therefrom.
A previously proposed measuring apparatus (see U.S. patent application Ser. No. 08/748,325) has been designed to make it possible to obtain high resolution and high accuracy irrespective of the density of picture elements. The thin strip of light beams U used in this apparatus is thick enough to vertically cover approximately five picture elements on the image pickup surface S2. One of these five picture elements on which the largest quantity of light is assumed to be incident, together with two picture elements which are disposed right over and right beneath the aforesaid one respectively, is used for interpolation for finding a position on which the largest quantity of light is actually incident. This position is hereinafter referred to as a "peak position", which determines the aforesaid light-emitting angle .theta.a made by the thin strip of light beams U. By virtue of the interpolation, the moment at which the peak position is found can fall within one of several sections into which the time interval between the sampling times n-1 and n (FIG. 5(b)) is divided.
Noise, which may be contributed to the output signal of the image pickup means, results from the distortion of a lens, wrong focusing, or the characteristic of an optical system. In the absence of noise, the distribution of the quantity of light in a direction which is perpendicular to a virtual plane formed by the thin strip of light beams U is normal as shown in FIG. 5(a). Noise causes serious departure from a normal distribution of the quantity of light, and a skewed, bimodal or flat distribution occurs, which constitutes one of the sources of error in the aforesaid previously proposed apparatus. A skewed distribution is especially apt to occur when the distribution of the quantity of light in the immediate vicinity of the peak position is nearly flat, e.g., when the thin strip of light beams incident on the image pickup element is thickened by the light-receiving optical system zoomed in the direction of the long-range focus, or when the departure from a normal distribution takes the form of a flat peak which results from the construction of the light-emitting optical system.
The aforesaid problem may be solved if the quantities of light obtained over a sufficiently long period of time before and after passage through the assumed peak position are used for interpolation. However, this attempt will necessitate the use of a complicated electrical circuit.